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allen-proxmire/prime-geometry: Prime Geometry I: The Prime Triangle Identity and Its Consequences (v1.0) Open

allen-proxmire · 2025

This release contains Prime Geometry I: The Prime Triangle Identity and Its Consequences, the foundational document of the Prime Geometry framework. Prime Geometry I establishes the exact algebraic–geometric identity relating consecutive p…

Paper 5 - Circular Prime Symmetry: Closed Rotational Orbits in the Prime System v0.1 Open

Clawson, Raymond, SAI, via HMI · 2025

Circular Prime Symmetry introduces the first fully characterizable coherence-stable species inside the prime landscape. A circular prime is a prime that remains prime under all cyclic rotations of its digits, forming a closed rotational or…

Paper 5 - Circular Prime Symmetry: Closed Rotational Orbits in the Prime System v0.1 Open

Clawson, Raymond, SAI, via HMI · 2025

Circular Prime Symmetry introduces the first fully characterizable coherence-stable species inside the prime landscape. A circular prime is a prime that remains prime under all cyclic rotations of its digits, forming a closed rotational or…

Commutative rings with $n$-$1$-absorbing prime factorization Open

Khalfi, Abdelhaq El, Laarabi, Hicham, Koç, Suat · 2025

Let $R$ be a commutative ring with $1\neq 0$ and $n$ be a fixed positive integer. A proper ideal $I$ of $R$ is said to be an \textit{$n$-OA ideal} if whenever $a_1a_2\cdots a_{n+1}\in I$ for some nonunits $a_1,a_2,\ldots,a_{n+1}\in R$, the…

On Square-Closed Lie Ideals and Generalized Homoderivations in Prime Rings Open

G. Naga Malleswari, S. Sreenivasulu, G. Naga Malleswari, S. Sreenivasulu · 2025

Let M be a square-closed noncentral Lie ideal of a prime ring R with char(R) ≠ 2. An additive mapping G on R is defined as a generalized homoderivation if it satisfies G(στ) = G(σ) h(τ) + G′(σ) y + x h(τ) for all σ and τ in R. This paper f…

Topological Divisibility and Prime Ideal Architectures Open

SÉRGIO DE ANDRADE, PAULO · 2025

This paper explores the theoretical synthesis between the concept of topological divisibility and the structural properties of prime ideal spaces in commutative rings. We introduce topological divisibility as a generalization of standard a…

Topological Divisibility and Prime Ideal Architectures Open

SÉRGIO DE ANDRADE, PAULO · 2025

This paper explores the theoretical synthesis between the concept of topological divisibility and the structural properties of prime ideal spaces in commutative rings. We introduce topological divisibility as a generalization of standard a…

Prime Spectra of Group Rings over Valued Fields Open

SÉRGIO DE ANDRADE, PAULO · 2025

This paper investigates the prime spectra of group rings formed over valued fields, an area that bridges the classical theories of group rings, valuation theory, and non-commutative algebra. While the prime spectrum of group rings over ord…

Prime Spectra of Group Rings over Valued Fields Open

SÉRGIO DE ANDRADE, PAULO · 2025

This paper investigates the prime spectra of group rings formed over valued fields, an area that bridges the classical theories of group rings, valuation theory, and non-commutative algebra. While the prime spectrum of group rings over ord…

Prime Spectra of Group Rings over Valued Fields Open

SÉRGIO DE ANDRADE, PAULO · 2025

This paper investigates the prime spectra of group rings formed over valued fields, an area that bridges the classical theories of group rings, valuation theory, and non-commutative algebra. While the prime spectrum of group rings over ord…

Topological Divisibility and Prime Ideal Architectures Open

SÉRGIO DE ANDRADE, PAULO · 2025

This paper explores the theoretical synthesis between the concept of topological divisibility and the structural properties of prime ideal spaces in commutative rings. We introduce topological divisibility as a generalization of standard a…

Derivations of Prime Rings and Their Action on Lie Ideals: A Structural Analysis Open

S. Lalitha · 2025

This paper presents a comprehensive structural analysis of derivations acting on Lie ideals in prime rings, investigating their fundamental properties and characterizations. We examine how derivations interact with Lie ideals, focusing on …

Identities related to generalized derivations on ideals in prime rings Open

V. K. Yadav V. K. Yadav, Sharad Sharma · 2025

On Jordan ideals and semigroup ideals in 3-prime near-rings with multiplicative derivations Open

Slimane El Amrani, Abderrahmane Raji · 2025

The aim of this article is to prove certain properties of multiplicative derivations verifying certain algebraic identities on Jordan ideals and semigroup ideals of a 3prime near-ring. The results obtained characterize the relationship bet…

Graded 1-Absorbing Prime Ideals over Non-Commutative Graded Rings Open

Azzh Saad Alshehry, Rashid Abu-Dawwas, Rahaf Abudalo · 2025

In this article, we define and study graded 1-absorbing prime ideals and graded weakly 1-absorbing prime ideals in non-commutative graded rings as a new class of graded ideals that lies between graded prime ideals (graded weakly prime idea…

REMARKS ON PRIME IDEALS AND REDUCED RINGS Open

Tae-Hee Lee, Zhelin Piao, Shengbin Wu · 2025

We first prove that a ring is prime if and only if whenever for a nonzero proper ideal of and . Then, by using this result, we give another proof of the well known fact that is prime if and only if the polynomial ring over is prime, We als…

Specific Identities Involving Prime Ideals with Generalized $P$-derivations Open

Radwan M. Al-omary, Ali Yahya Hummdi, Zakia Z. Al-Amery · 2025

In this article, we will investigate the commutativity of the factor ring $\Re/P$, where $P$ is a prime ideal of any ring $\Re$. This investigation will be carried out using generalized $P$-derivations $\mho$ and $\amalg$ associated with $…

Maximal Prime Ideals in Generalized Almost Distributive Fuzzy Lattices Open

T. Sangeetha · 2025

The Maximal Prime Ideals (MPIs) in Generalized Almost Distributive Fuzzy Lattices are presented in this article (GADFL). In GADFL, we have also deduced certain properties and characteristic theorems of MPIs. Further, we have also derived t…

Action of multiplicative (generalized)-derivations and related maps on square closed Lie ideals in prime rings Open

Basudeb Dhara · 2025

Let $\mathcal{R}$ be a prime ring and $L$ a nonzero square closed Lie ideal of $\mathcal{R}$. Suppose $F,G,H\colon \mathcal{R}\to \mathcal{R}$\break are three multiplicative (generalized)-derivations associated with the maps $\delta,g, h\c…

On Prime Ideals in Rings Satisfying Certain Functional Identities Open

Kholood Alnefaie, Radwan M. Al-omary · 2025

In this note, we will examine the relationship between a generalized derivation ϝ associated with a derivation ∂ that satisfies specific algebraic identities and the behavior of a factor ring S/P, where P is a prime ideal of any ring S. We…

Jordan Generalized Higher Symmetric Reverse Bi-Derivations on Prime Γ-Rings Open

Jafar Salih, Salah Mehdi Salih · 2025

In this paper we show that, every Jordan generalized higher symmetric reverse bi-derivations is a generalized higher symmetric reverse bi-derivations on a ring M. Additionally, a generalized higher symmetric reverse is Jordan generalized h…

A Study of Generalized Differential Identities via Prime Ideals Open

Ali Yahya Hummdi, K. Charrabi, Shakir Ali, Abdellah Mamouni · 2025

Let be a ring and be a prime ideal of . The aim of this research paper is to delve into the relationship between the structural properties of the quotient ring and the behavior of generalized derivations in a ring endowed with an involutio…

On the structure and applications of neutrosophic prime ideals Open

Ali Yahya Hummdi, A. Elrawy · 2025

This study explores key characteristics associated with neutrosophic prime ideals. In particular, it is shown that the image corresponding to these ideals contains exactly two different elements. The work also extends the concept of classi…

On 2-absorbing ideals of MV-algebras Open

Asiyeh Hassani Movahed, Mahta Bedrood, Arsham Borumand Saeid · 2025

The concept of 2-absorbing ideals in MV-algebras, which generalizes the notion of prime ideals, is introduced in this paper. We present several results related to 2-absorbing ideals, provide examples, and explore some of properties. One no…

Effects of Generalized Semiderivations on Algebraic Identities Involving Prime Ideals Open

Kholood Alnefaie · 2025

In this article, instead of a generalized derivation, we will use the concept of a generalized semiderivation ∇ that satisfies various identities involving a prime ideal ß of an optional ring Λ to describe the behavior of a quotient ring Λ…

A Pair of Generalized (α, α)‐Derivations With Identities Related to Prime Ideals Open

Ali Yahya Hummdi, Hafedh Alnoghashi, Radwan Mohammed Al-Omary, Abdelkarim Boua, Ali Yahya Hummdi , et al. · 2025

Let be an arbitrary ring, α an automorphism of , a nonzero ideal of , and ϒ a prime ideal of satisfying the condition . This research investigates the interplay between two generalized ( α , α )‐derivations, Ω and (associated with ( α , α …

Normally torsion-freeness and normality criteria for monomial ideals Open

Mehrdad Nasernejad, Veronica Crispin Quiñonez, Jonathan Toledo · 2025

In this paper, we focus on the associated primes of powers of monomial ideals and asymptotic behavior properties such as normally torsion-freeness, normality, the strong persistence property, and the persistence property. In particular, we…

Ordered semigroups in which primeideals are maximal Open

Pisan Summaprab · 2025

e-Prime Ideals of Commutative Rings Open

Omar A. Abdullah, Ali Sh. Ajeel, Mohmad E. Dahash · 2025

In this paper, all rings will be commutative with identity. We let ID(R) denote the set of all idempotents of R. In recent years, many generalizations of the concept of prime ideal have been studied such as weakly prime ideals \cite{Anders…

On Soft Near‐Prime Int‐Ideals and Soft 1‐Absorbing Prime Int‐Ideals With Applications Open

İbrahim Halil Kanat, Filiz Çıtak · 2025

In this study, we aimed to introduce two different generalizations of the soft prime int‐ideal and clarify the relationships between the soft prime int‐ideal and the substructures of a ring. First, we explored new algebraic features of the…

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